Name: beam forces: tension, shear, and bending
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Lorsqu’une poutre est soumise à une charge, elle subit des forces internes qui peuvent être classées en moments normaux, de cisaillement et de flexion.
Les efforts internes peuvent être déterminés à l’aide de la méthode des sections. Une convention de signe spéciale est appliquée car ils se produisent par paires, et leur direction dépend du côté de la section à analyser.
La force normale est considérée comme positive si elle crée une tension, tandis qu’elle est considérée comme négative si elle génère une compression dans l’objet.
Supposons que les forces agissant tangentiellement à la section transversale soient dirigées vers le bas et vers le haut sur les côtés gauche et droit de la section, respectivement. Dans ce cas, la force de cisaillement est considérée comme positive, ce qui entraîne une rotation dans le sens des aiguilles d’une montre.
De même, si la direction des forces de chaque côté est inversée, un cisaillement négatif est produit, ce qui entraîne une rotation dans le sens inverse des aiguilles d’une montre.
Lorsqu’une force externe agit sur le faisceau, celui-ci subit un moment de flexion, formant une courbure concave vers le haut ou vers le bas. Le moment de flexion est positif pour la courbure vers le haut et négatif pour la courbure vers le bas.

<ol>
	<li>Ferdinand Beer, E. Johnston, David Mazurek, Phillip Cornwell et Brian Self (2019). Mécanique vectorielle pour les ingénieurs : statique et dynamiques. McGraw Hill. Pages 380 et 391.</li>
	<li>Russell C. Hibbeler. (2016). Mécanique de l’ingénierie : statique et dynamique. Pearson. p. 343 à 345.</li>
</ol>

convention de signe

Sign Convention

Lors de l'analyse d'une poutre soumise à différentes charges, il est crucial de comprendre les forces internes et les moments générés à l'intérieur de la structure. Ces forces internes peuvent être largement classifiées en forces normales, forces de cisaillement et moments de flexion. Pour déterminer ces forces et moments, nous utilisons la méthode des sections et appliquons une convention de signe spécifique en fonction de leur direction et du côté de la section analysée. La force normale agit perpendiculairement à la section transversale de la poutre et peut causer une tension ou une compression dans l'objet. Lorsque la force normale crée une tension, on suppose qu'elle est positive, tandis que lorsqu'elle génère une compression, elle est considérée comme négative. La force de cisaillement fait référence aux forces agissant tangentiellement à la section transversale de la poutre. Ces forces apparaissent généralement par paires, avec une force agissant du côté gauche de la section et l'autre du côté droit. Si la force du côté gauche est dirigée vers le bas et la force du côté droit est dirigée vers le haut, la force de cisaillement est considérée comme positive, entraînant une rotation dans le sens des aiguilles d'une montre. En revanche, si la direction des forces de chaque côté est inversée, une force de cisaillement négative est produite, entraînant une rotation dans le sens inverse des aiguilles d'une montre. Le moment de flexion est l'effet de rotation causé par une force externe agissant sur la poutre. Lorsqu'elle est soumise à une telle force, la poutre subit une courbure, pouvant être vers le haut (concave) ou vers le bas (convexe). La convention de signe des moments de flexion stipule qu'un moment de flexion positif correspond à une courbure vers le haut (concave), tandis qu'un moment de flexion négatif correspond à une courbure vers le bas (convexe). Cette convention joue un rôle essentiel dans la compréhension du schéma de déformation de la poutre et dans la conception d'éléments structuraux appropriés pour résister à la flexion. En résumé, les conventions de signe pour la force normale, la force de cisaillement et le moment de flexion sont des outils essentiels en analyse structurale. Elles aident les ingénieurs et les concepteurs à comprendre le comportement des structures sous différentes charges, à prévoir les modes de défaillance potentiels et à concevoir des éléments structuraux robustes et efficients.

Convention de signe

Lors de l’analyse d’une poutre soumise à diverses charges, il est crucial de comprendre les forces et les moments internes générés à l’intérieur de la structure. Ceux-ci...

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beam forces: tension, shear, and bending

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative.

Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it easier to read and compare force results during structural analysis.

Shear force acts tangentially along the cross-section of the beam. It often appears as a pair of forces, with one side of the cut carrying the left-side force and the other side carrying the right-side force. A downward force on the left side and an upward force on the right side represent positive shear and a clockwise rotation. If the directions are reversed, the shear force is negative and the rotation is counterclockwise.

Bending moment describes the turning effect created by an external force on a beam. It changes the beam’s shape into either an upward, concave curve or a downward, convex curve. A positive bending moment gives upward, concave curvature. A negative bending moment gives downward, convex curvature. These conventions help predict how beams deform under load and support better structural design.

Beam Forces: Tension, Shear, and Bending

sign convention

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative. Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it...

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key terms and concepts

Learn how normal force, shear force, and bending moment use sign conventions in beam analysis, and how tension, compression, and curvature are labeled.

Beam Forces: Tension, Shear, and Bending | JoVE K12

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mechanical engineering

Beam Forces: Tension, Shear, and Bending

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